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Even powers of divisors and elliptic zeta values

Felder, Giovanni ; Varchenko, Alexander

In: Journal für die reine und angewandte Mathematik, 2005, vol. 2005, no. 579, p. 195-201

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    Title
    • Even powers of divisors and elliptic zeta values
    Author
    • Felder, Giovanni. MSRI, 1000 Centennial Drive, Berkeley, CA 94720, USA; Departement of Mathematics, ETH-Zentrum, 8092 Zürich, Switzerland.
    • Varchenko, Alexander. Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA.
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:302579
    Summary
    We introduce and study elliptic zeta values, a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coeffcients of the logarithm of the elliptic gamma function, and inherit the functional equations of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisors. The elliptic zeta values at odd integers can be expressed in terms of generating series of sums of even powers of divisors